The invention disclosed and claimed herein generally pertains to a method of magnetic resonance (MR) imaging, wherein acquired MR data has an associated linear phase shift which must be determined to reduce image artifacts, improve image quality or as a measure of some physical quantity. More particularly, the invention pertains to a method of the above type which significantly improves or enhances efficiency in determining linear phase shift. Even more particularly, the invention pertains to a method of the above type wherein MR data is acquired in one domain, such as the time domain, and the associated linear phase shift is determined in a domain conjugate thereto, such as the frequency domain.
As is well known by those of skill in the art, acquired MR image data may comprise complex valued signals, such as data acquired by sampling an MR signal in quadrature. Each data sample then comprises a complex value having an associated magnitude and phase. Complex valued signals are often considered to have two equivalent representations, referred to as the time domain and frequency domain representations, respectively.
As is further well known, certain MR imaging techniques require determination of linear or first order phase shift, that is, the variation of phase between adjacent MR data samples in a set of MR data. For example, linear phase shift is used in connection with a technique known as navigator echo, to determine the position of selected body structure of a patient which is subject to periodic or cyclical respiratory motion. Such positional information is essential, in order to minimize artifacts in providing an image of the moving structure. Typically, body structure associated with respiration comprises a patient's diaphragm, as well as organs such as the lungs and liver which move with the diaphragm. Such information is particularly useful for coronary artery MR imaging and general abdominal body MR imaging.
One such navigator echo technique, described in an article by Foo et al entitled "Navigator and Linear Phase Shift Processing", Proceedings of ISMRM, page 323 (1998), is based on the Fourier Transform Shift Theorem. Such technique is also described in U.S. patent application Ser. No. 08/980,192, filed Nov. 26, 1997 by Foo et al, and issued as U.S. Pat. No. 6,067,465 on May 23, 2000, which is commonly assigned herewith to the General Electric Company. In accordance with the Fourier Transform Shift Theorem, if an object centered about the origin of a coordinate system is displaced in a specified direction, then the Fourier transform of a function defining the object will have a linear phase shift that is equivalent to the amount of spatial displacement. Thus, in the Foo et al technique, a navigator echo signal associated with a moving structure of interest is acquired in the time domain. The acquired navigator echo is then Fourier transformed into the frequency domain, to provide a corresponding frequency profile or spectrum. The spectrum is truncated or apodized, such as by means of a band limiting filter, to remove any extraneous signal components. The truncated frequency profile is then Fourier transformed back to the time domain. Thereupon, linear phase shift is determined in the time domain, preferably by means of the Ahn algorithm. The position of the structure of interest, at the acquisition time of the navigator echo, may then be readily computed. The Ahn algorithm is a very well known technique for determining linear phase shift of a complex valued signal, and is described, for example, in "A New Phase Correction Method in NMR imaging based on Auto Correlation and Histogram Analysis", Ahn, et. al., IEEET Trans. Med. Imaging, 1987: MI-6: 32-36.
While the Ahn algorithm is known to be very computationally efficient, it will be seen that the navigator echo technique described above requires a Fourier transformation operation, from the frequency domain back to the time domain, before the Ahn algorithm can be applied. It would significantly enhance computational efficiency even further, if linear phase shift could be determined directly from frequency domain data so that the transformation back to the time domain would be unnecessary. In addition, certain multi-echo image sequences, such as echo planar imaging (EPI) and fast spin echo (FSE), also require determination of linear phase shift of the frequency domain spectrum (obtained from the time domain echo signal by Fourier transformation), for use in phase correction. In certain applications associated with these sequences, linear phase shift must be computed in near-real time, in order to provide phase correction of the multi-echo signals as image acquisition and reconstruction is being carried out. For these applications also, it would be very useful to be able to determine linear phase shift from data directly available in one domain, and to thus avoid the need to perform a Fourier transform back to the other domain. Significant reduction in processing time could thereby be achieved.